W. V. O. Quine in "On What There Is?" denies the existence of universals. There are red things, like a fire truck (f), a tomato (t), a red umbrella (u). But the phrase "They have redness in common" is in his view just a manner of speech, in which redness does not refer to an actual entity (a universal). Instead it just means that the predicate R(x) = "x is red" can be applied to them all: R(f) ∧ R(t) ∧ R(u).
Quine managed to paraphrase the claim without some existential claim occurring. So according to his standard, his ontological theory does not commit to the existence of universals.
But as Howard Peacock notices, we also talk about things just having something in common (indeterminate). Two things a and b having something in common seems to mean ∃P: P(a) ∧ P(b) with P being a predicate and so "existence" again. We would have to say that just a formula like P(a) ∧ P(b) applies to avoid the existential quantifier.
Yet if we have two things a and b for which it is true that a is unlike anything else, and b is unlike anything else, this predicate of U(x) = "x is unlike anything else" can be both applied to them: U(a) ∧ U(b). But it seems wrong to state that a and b have something in common.
So at least at this point, Quine's translation probably does not catch the original meaning of the phrase; we distinguish between aspects of a thing (that play a role in the concept of "being like") and just any random predicate which applies to things.
If we don't find a simple way out of that, couldn't we just say that Quine's translation of "have something in common" does not apply to any predicate but only to certain special predicates? Maybe we can't give a definition for those special predicates, but do we have to?
As we see from the discussion there are two issues:
(a) How do we handle existence claims that occur when the paraphrasing method is defined? Like above "a formula like" seems to commit to types (of formulas). But if the paraphrase method succeeds wouldn't it also be able to paraphrase the method itself?
(b) Can an "incomplete" ontological theory be judged to commit to certain entities for which existence claims are made but no fully generalized paraphrasing method is available -- or not?
It seems that the avoidance to tackle the question what "is" means just postpones it. It emerges later again, in a more obscure way. (a) and (b) seem just convoluted ways to ask: "What do you mean by 'is'?".
On the other way around, if our theory admits that there is a subset of predicates that work like universals, may this not be just close enough to metaphysical realism for all purposes? What does it even matter if we get around using an existence claim?
Should we not explore if the existence claim of metaphysical realism has any further content than "like" sometimes being objective, found in the nature of things, and sometimes not?
So how can anything of importance be gained from Quine's method, which refuses to engage with the meaning of "is"? Ignoring the meaning of "is" / "exists" and just shuffling words around until the offending word does not occur anymore -- what did Quine try to achieve with that?